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He completed an S.B. and S.M. in Mathematics at the Massachusetts Institute of Technology in 1972.[1] The title of his thesis was "Evaluation of certain character sums".[1] He was a Putnam Fellow at MIT in 1970.[1] He received his Ph.D. in Mathematics from MIT for his thesis "The 4-part of the class group of a quadratic field", in 1974.[1][2] His advisor for both his masters and Ph.D was Harold Stark.[1]

In 1975 he joined AT&T Bell Laboratories and eventually became Distinguished Member of Technical Staff. Since 1995, he has been a Technology Consultant at AT&T Research Laboratories. In 2002, he moved to Michigan to work at the University and settle down with his family.

While his recent work has been in theoretical computer science, his original training was in analytic algebraic number theory. He has since worked in many areas, both pure and applied, and considers himself a mathematical generalist. Lagarias discovered an elementary problem that is equivalent to the Riemann hypothesis, namely whether
for all n > 0, we have